Observer‐based adaptive neural control for a class of nonlinear singular systems

Abstract

The problem of observer-based adaptive neural control via output feedback for a class of uncertain nonlinear singular systems is studied in this article. The nonlinear singular systems can be regarded as two subsystems that are coupled with each other: differential subsystem and algebraic subsystem. The differential systems can be nonstrict feedback structures. To guarantee that the singular system is regular and impulse-free, two new conditions are proposed. By the conditions, the linear controller and observer, which are used to estimate the immeasurable state variables, are obtained. Then, an output feedback scheme through adaptive neural backstepping is proposed to ensure that all states of the closed-loop system are semiglobally uniformly ultimately bounded and converge to a small neighborhood of the origin. Simulation examples illustrate the effectiveness of the presented method. K E Y W O R D S adaptive neural control, output feedback, singular system, uncertain nonlinear system 1 Int J Robust Nonlinear Control. 2020;30:4043-4058. wileyonlinelibrary.com/journal/rnc © 2020 John Wiley & Sons, Ltd. 4043 4044 CHEN et al.nonstrict feedback systems. 11 In addition, the Newton-based observer, 19 sliding-mode, 20 and Lyapunov-based observer 21 are designed for nonlinear systems. Singular systems have been extensively studied because it can better describe the physical systems, such as power systems, economics, biological systems, and other areas. 22,23 The study of singular systems is much more complicated than that of the state-space systems because not only the stability but also the regularity and impulse-free should be considered. Recently, the study of singular systems is mainly based on the linear system theory. The observer design is addressed in References 24-27. The problems of stability analysis for singular Markovian jump systems, 28 and the admissibility for singular T-S fuzzy model 29 are studied. In References 30 and 31 , the analysis and control synthesis for singular systems with time delays are discussed. All the above results are based on linear matrix inequality (LMI) techniques. The above methods are regarded as effective methods for linear singular systems. However, for nonlinear, or uncertain singular systems, the T-S fuzzy model-based methods 22,32-34 will bring much conservatism. It is known that the control problems for normal uncertain nonlinear systems can be solved to some extent by the advanced adaptive control theory. And the adaptive control theory has been extended to solve the admissibility problems for nonlinear singular systems in References 35-37. Nevertheless, for the more complex uncertain nonlinear singular systems, and more complex control problems, such as nonlinear tracking control, a better way should be developed.In this article, an observer-based neural control scheme via output feedback is proposed for a class of uncertain nonlinear singular systems for the first time. In the proposed scheme, a reduced-order observer is constructed to estimate the unmeasured state vari...

State and adaptive disturbance observer co‐design for incrementally quadratic nonlinear descriptor systems with nonlinear outputs

“…It is worth pointing out that descriptor systems are becoming more and more complex and often exhibit nonlinear characteristics. Whereas, the existing research 8‐16 mainly focuses on such systems with specific structured nonlinearities. For example, in Reference 10, the authors have provided an observer design framework for one‐sided Lipschitz descriptor systems with nonlinearities in the output and state equations.…”

“…It is interesting to note that most of the nonlinearities mentioned in the above works 8‐16 can be expressed in terms of incremental quadratic constraints ($$$ \delta $$$QC) parameterized by a bunch of incremental multiplier matrices ($$$ \delta $$$MMs) proposed by D'Alto and Corless 17 . $$$ \delta $$$QC can provide a framework for various common classes of nonlinearities.…”

“…$$$ \delta $$$QC can provide a framework for various common classes of nonlinearities. In other words, various types of nonlinearities can be seen as a particular case of $$$ \delta $$$QC by selecting appropriate $$$ \delta $$$MMs, such as nonlinearities satisfying monotone, 14 quadratic inequality, 16 incremental bounded sector conditions, 8,9,17 quadratic inner‐bounded conditions, 11 Lipschitz conditions, 13,15 one‐sided Lipschitz conditions 10‐12 and more. Recently, the investigation for systems satisfying $$$ \delta $$$QC has yielded fruitful results 18‐26 .…”

“…However, in practical engineering applications such as secure communication, the output of the system is often nonlinear. And numerous works 8,19,20,32,34,36‐38 have focused on addressing observer design problems using adaptive control theory. Therefore, how to design the state observer and adaptive disturbance observers for incrementally quadratic nonlinear descriptor systems with output nonlinearities remains an open research topic.…”

Observer‐based adaptive neural networks control for Markovian jump nonlinear systems with partial mode information and input saturation

“…Liang et al 35 designed reduced‐order observers for stochastic nonlinear multi‐agent systems. It should be pointed out that the observer‐based control is one of effective and convenient methods to estimate state variables, which only need the input and output signals of systems 12,28,34,36–39 . For example, the authors 12 studied slide mode control issue for MJSs and constructed state observer to estimate unavailable state variables, in which the Markov mode information was involved in the observer.…”